Dual-comb spectroscopy performed in the mid-infrared—where molecules have their strongest rotovibrational absorption lines—offers the promise of high spectral resolution broadband spectroscopy with very short acquisition times (μs) and no moving parts. Recently, we demonstrated frequency comb operation of a quantum-cascade-laser. We now use that device in a compact, dual-comb spectrometer. The noise properties of the heterodyne beat are close to the shot noise limit. Broadband (15 cm−1) high-resolution (80 MHz) absorption spectroscopy of both a GaAs etalon and water vapour is demonstrated, showing the potential of quantum-cascade-laser frequency combs as the basis for a compact, all solid-state, broadband chemical sensor. The fundamental vibrational bands of many molecules lie on the mid-infrared, so generating all solid-state, compact frequency combs in that region is important for molecular spectroscopy. Here, Villares et al.use quantum-cascade-laser frequency combs to demonstrate a high resolution, broadband dual-comb spectrometer.